Geometric vs Componentwise Vector Addition

[linie18]

Homework Statement

Which of following sets of conditions (A - F), if true, would show that the expressions 1 and 2 above define the same vector C_vec as expressions 3 and 4?

1. The two pairs of expressions give the same length and direction for C_vec.
2. The two pairs of expressions give the same length and x component for C_vec.
3. The two pairs of expressions give the same direction and x component for C_vec.
4. The two pairs of expressions give the same length and y component for C_vec.
5. The two pairs of expressions give the same direction and y component for C_vec.
6. The two pairs of expressions give the same x and y components for C_vec.

Homework Equations

1. C=\sqrt{A^2 +B^2 -2 A B \cos(c)},
2. \phi = \sin^{-1}\left(\frac{B\sin(c)}{C}\right).
3. C_x = A + B\cos(\theta),
4. C_y = B\sin(\theta).

The Attempt at a Solution

I thought it would be one where you knew exactly what the vector was like AF and I don't know what I'm missing.

 

[quantumdude]

Which of following sets of conditions (A - F), if true, would show that the expressions 1 and 2 above[/color] define the same vector C_vec as expressions 3 and 4?

Haven't you forgotten to include something[/color]?

 

[gbloomq]

whats the answer?

 

[LearninDaMath]

Any suggestions or answers on this problem yet? I'm having confusion on the same exact problem. I'm trying to search for help for on this problem. It seems to be a confusing one to answer.